From what I understand, CMB is the left over radiation from the Big Bang. As all matter, including the Earth, was made during the Big Bang and then as the universe expanded that matter/energy got further and further apart, but as that matter can't move faster than the speed of light then we should be behind the CMB which travels at the speed of light. So from my understanding the CMB would have passed us and most of the matter of the universe a long time ago so we shouldn't be able to detect it. Also on a side note how is the CMB constant; shouldn't it be a flash? Sorry if the question doesn't make much sense. I am a student so please use layman's terms.
[Physics] How to detect cosmic background radiation
cosmic-microwave-backgroundcosmic-raysmicrowavesradiation
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The cosmic microwave background does not originate with the big bang itself. It originates roughly 380,000 years after the big bang, when the temperature dropped far enough to allow electrons and protons to form atoms. When it was released, the cosmic microwave background wasn't microwave at all- the photons had higher energies. Since that time, they have been redshifted due to the expansion of the universe, and are presently in the microwave band.
The universe is opaque from 380,000 years and earlier. The galaxies that we can see only formed after that time. Before that, all that is observable is the CMB.
It is unlikely that we can detect gravitational waves from the Big Bang with current technology. Due to universal expansion, such waves would have very large wavelengths.
We would need interferometers that are thousands, perhaps millions, of kilometers long to detect them. The LIGO observatory simply would not be sufficient. To put things into perspective, consider that the arms of the LIGO interferometer have a length of $4km$. But it is important to note that the effective LIGO arm length is $1600km$ (the light beam inside the interferometer is reflected back and forth 400 times) and LIGO is most "sensitive" at a frequency of about $150Hz$, which would correspond to a wavelength of $\lambda \approx 2000km$ meaning the LIGO arms have a length of $\approx\frac{\lambda}{2}$.
do we have the technology to detect them in the foreseeable future?
There is a proposal called "LISA" that will involve a system of satellites in space separated by large distances ($\gt 10^6$ km), that could possibly detect gravitational waves (gravitational waves that where emitted before the photon epoch - up to 380,000 years after the Big Bang as you mentioned).
From that link:
"The Laser Interferometer Space Antenna (LISA) is a proposed space probe to detect and accurately measure gravitational waves—tiny ripples in the fabric of spacetime—from astronomical sources. LISA would be the first dedicated space-based gravitational wave detector. It aims to measure gravitational waves directly by using laser interferometry. The LISA concept has a constellation of three spacecraft arranged in an equilateral triangle with sides 2.5 million kilometres long, flying along an Earth-like heliocentric orbit. The distance between the satellites is precisely monitored to detect a passing gravitational wave...
Potential sources for signals [that LISA could detect] are merging massive black holes at the center of galaxies, massive black holes orbited by small compact objects, known as extreme mass ratio inspirals, binaries of compact stars in our Galaxy, and possibly other sources of cosmological origin, such as the very early phase of the Big Bang , and speculative astrophysical objects like cosmic strings and domain boundaries."
Best Answer
You are assuming the Big Bang happened at a point, so the CMB is a shell of radiation expanding outwards from that point. However the Big Bang happened everywhere so every point in the universe is a source of the CMB. The CMB radiation we are detecting today comes from regions of the universe that were about 13.8 billion light years away at the moment the CMB was emitted (those points are a lot farther away now).
The fact that the Big Bang happened everywhere is a difficult conceptual issue for non-physicists. See my answer to the question Was the singularity at Big Bang perfectly uniform and if so, why did the universe lose its uniformity? for a non-physicist friendly discussion of this.